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636 lines
23 KiB
Fortran
636 lines
23 KiB
Fortran
!!$
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!!$ MLD2P4
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!!$ MultiLevel Domain Decomposition Parallel Preconditioners Package
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!!$ based on PSBLAS (Parallel Sparse BLAS v.2.0)
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!!$
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!!$ (C) Copyright 2006 Alfredo Buttari University of Rome Tor Vergata
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!!$ Pasqua D'Ambra ICAR-CNR, Naples
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!!$ Daniela di Serafino Second University of Naples
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!!$ Salvatore Filippone University of Rome Tor Vergata
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!!$
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!!$ Redistribution and use in source and binary forms, with or without
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!!$ modification, are permitted provided that the following conditions
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!!$ are met:
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!!$ 1. Redistributions of source code must retain the above copyright
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!!$ notice, this list of conditions and the following disclaimer.
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!!$ 2. Redistributions in binary form must reproduce the above copyright
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!!$ notice, this list of conditions, and the following disclaimer in the
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!!$ documentation and/or other materials provided with the distribution.
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!!$ 3. The name of the MLD2P4 group or the names of its contributors may
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!!$ not be used to endorse or promote products derived from this
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!!$ software without specific written permission.
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!!$
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!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
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!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
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!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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!!$ POSSIBILITY OF SUCH DAMAGE.
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!!$
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!!$
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! File: mld_dilu_fct.f90.
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!
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! Subroutine: mld_dilu_fct.
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! Version: real.
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! Contains: mld_dilu_fctint, ilu_copyin
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!
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! Computes either the ILU(0) or the MILU(0) factorization of the local part
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! of the matrix stored into a. These factorizations are used to build the 'base
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! preconditioner' (block-Jacobi preconditioner/solver, Additive Schwarz
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! preconditioner) corresponding to a certain level of a multilevel preconditioner.
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!
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! Details on the above factorizations can be found in
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! Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition,
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! SIAM, 2003, Chapter 10.
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!
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! The local matrix to be factorized is stored into a and blck, as specified in
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! the description of the arguments below. The storage must be in CSR format.
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! The same format is used for the L and U factors. The diagonal of the U factor
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! is stored separately.
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!
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! This routine copies and factors "on the fly" from a and blck into l (L factor),
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! u (U factor, except its diagonal) and d (diagonal of U). This implementation of
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! ILU(0) is faster than the implementation in mld_diluk_fct (the latter routine
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! performs the more general ILU(n)).
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!
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!
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! Arguments:
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! ialg - integer, input.
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! The type of incomplete factorization to be performed.
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! The MILU(0) factorization is computed if ialg = 2 (= mld_milu_n_);
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! the ILU(0) factorization otherwise.
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! a - type(<psb_dspmat_type>), input.
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! The sparse matrix structure containing the local matrix to be
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! factorized. Note that if the 'base' Additive Schwarz preconditioner
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! has overlap greater than 0 and the matrix has not been reordered
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! (see mld_bjac_bld), then a contains only the 'original' local part
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! of the matrix to be factorized, i.e. the rows of the matrix held
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! by the calling process according to the initial data distribution.
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! l - type(<psb_dspmat_type>), input/output.
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! The L factor in the incomplete factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! u - type(<psb_dspmat_type>), input/output.
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! The U factor (except its diagonal) in the incomplete factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! d - real(kind(1.d0)), dimension(:), input/output.
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! The diagonal of the U factor in the incomplete factorization.
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! Note: its allocation is managed by the calling routine mld_ilu_bld,
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! hence it cannot be only intent(out).
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! info - integer, output.
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! Error code.
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! blck - type(<psb_dspmat_type>), input, optional, target.
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! The sparse matrix structure containing the remote rows of the
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! matrix to be factorized, that have been retrieved by mld_asmat_bld
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! to build an Additive Schwarz base preconditioner with overlap
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! greater than 0. If the overlap is 0 or the matrix has been reordered
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! (see mld_bjac_bld), then blck is empty.
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!
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subroutine mld_dilu_fct(ialg,a,l,u,d,info,blck)
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use psb_base_mod
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use mld_prec_mod, mld_protect_name => mld_dilu_fct
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implicit none
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! Arguments
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integer, intent(in) :: ialg
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type(psb_dspmat_type),intent(in) :: a
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type(psb_dspmat_type),intent(inout) :: l,u
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real(kind(1.d0)), intent(inout) :: d(:)
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integer, intent(out) :: info
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type(psb_dspmat_type),intent(in), optional, target :: blck
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! Local variables
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real(kind(1.d0)) :: dia, temp
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integer :: i, j, jj, k, kk, l1, l2, ll, low1, low2,m,ma,err_act
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type(psb_dspmat_type), pointer :: blck_
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character(len=20) :: name, ch_err
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logical, parameter :: debug=.false.
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name='mld_dilu_fct'
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info = 0
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call psb_erractionsave(err_act)
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!
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! Point to / allocate memory for the incomplete factorization
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!
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if (present(blck)) then
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blck_ => blck
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else
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allocate(blck_,stat=info)
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if (info /= 0) then
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call psb_errpush(4010,name,a_err='Allocate')
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goto 9999
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end if
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call psb_nullify_sp(blck_) ! Probably pointless.
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call psb_sp_all(0,0,blck_,1,info)
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if(info.ne.0) then
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info=4010
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ch_err='psb_sp_all'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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blck_%m=0
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endif
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!
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! Compute the ILU or the MILU factorization, depending on ialg
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!
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call mld_dilu_fctint(ialg,m,a%m,a,blck_%m,blck_,&
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& d,l%aspk,l%ia1,l%ia2,u%aspk,u%ia1,u%ia2,l1,l2,info)
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if(info.ne.0) then
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info=4010
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ch_err='mld_dilu_fctint'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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!
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! Store information on the L and U sparse matrices
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!
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l%infoa(1) = l1
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l%fida = 'CSR'
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l%descra = 'TLU'
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u%infoa(1) = l2
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u%fida = 'CSR'
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u%descra = 'TUU'
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l%m = m
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l%k = m
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u%m = m
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u%k = m
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!
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! Nullify pointer / deallocate memory
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!
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if (present(blck)) then
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blck_ => null()
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else
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call psb_sp_free(blck_,info)
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if(info.ne.0) then
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info=4010
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ch_err='psb_sp_free'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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deallocate(blck_)
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endif
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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contains
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!
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! Subroutine: mld_dilu_fctint.
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! Version: real.
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! Note: internal subroutine of mld_dilu_fct.
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!
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! Computes either the ILU(0) or the MILU(0) factorization of the local part
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! of the matrix stored into a. These factorizations are used to build the 'base
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! preconditioner' (block-Jacobi preconditioner/solver, Additive Schwarz
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! preconditioner) corresponding to a certain level of a multilevel preconditioner.
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!
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! The local matrix to be factorized is stored into a and b, as specified in the
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! description of the arguments below.The output storage format for both L and U
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! factors is CSR. The diagonal of the U factor is stored separately in D.
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!
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! This routine copies and factors "on the fly" from the sparse matrix structures a
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! and b into the arrays laspk, uaspk, d (L, U without its diagonal, diagonal of U).
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!
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!
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! Arguments:
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! ialg - integer, input.
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! The type of incomplete factorization to be performed.
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! The MILU(0) factorization is computed if ialg = 2 (= mld_milu_n_);
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! the ILU(0) factorization otherwise.
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! m - integer, output
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! The total number of rows of the local matrix to be factorized,
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! i.e. ma+mb.
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! ma - integer, input
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! The number of rows of the local submatrix stored into a.
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! a - type(<psb_dspmat_type>), input.
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! The sparse matrix structure containing the local matrix to be
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! factorized. Note that, if the 'base' Additive Schwarz preconditioner
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! has overlap greater than 0 and the matrix has not been reordered
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! (see mld_bjac_bld), then a contains only the 'original' local part
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! of the matrix to be factorized, i.e. the rows of the matrix held
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! by the calling process according to the initial data distribution.
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! mb - integer, input
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! The number of rows of the local submatrix stored into b.
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! b - type(<psb_dspmat_type>), input.
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! The sparse matrix structure containing the remote rows of the
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! matrix to be factorized, that have been retrieved by mld_asmat_bld
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! to build an Additive Schwarz base preconditioner with overlap
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! greater than 0. If the overlap is 0 or the matrix has been reordered
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! (see mld_bjac_bld), then b does not contain any row.
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! d - real(kind(1.d0)), dimension(:), output
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! The diagonal of the U factor in the incomplete factorization.
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! laspk - real(kind(1.d0)), dimension(:), inout
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! The L factor in the incomplete factorization.
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! lia1 - integer, dimension(:), inout
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! The column indices of the nonzero entries of the L factor,
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! according to the CSR storage format.
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! lia2 - integer, dimension(:), inout
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! The indices identifying the first nonzero entry of each row
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! of the L factor in laspk, according to the CSR storage format.
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! uaspk - real(kind(1.d0)), dimension(:), inout
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! The U factor in the incomplete factorization.
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! The entries of U are stored according to the CSR format.
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! uia1 - integer, dimension(:), inout
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! The column indices of the nonzero entries of the U factor,
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! according to the CSR storage format.
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! uia2 - integer, dimension(:), inout
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! The indices identifying the first nonzero entry of each row
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! of the U factor in uaspk, according to the CSR storage format.
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! l1 - integer, output
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! The number of nonzero entries in laspk.
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! l2 - integer, output
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! The number of nonzero entries in uaspk.
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! info - integer, output.
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! Error code.
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!
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subroutine mld_dilu_fctint(ialg,m,ma,a,mb,b,&
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& d,laspk,lia1,lia2,uaspk,uia1,uia2,l1,l2,info)
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implicit none
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! Arguments
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integer, intent(in) :: ialg
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type(psb_dspmat_type) :: a,b
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integer :: m,ma,mb,l1,l2,info
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integer, dimension(:) :: lia1,lia2,uia1,uia2
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real(kind(1.d0)), dimension(:) :: laspk,uaspk,d
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! Local variables
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integer :: i,j,k,l,low1,low2,kk,jj,ll, irb, ktrw,err_act
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real(kind(1.d0)) :: dia,temp
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integer, parameter :: nrb=16
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logical,parameter :: debug=.false.
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type(psb_dspmat_type) :: trw
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integer :: int_err(5)
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character(len=20) :: name, ch_err
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name='mld_dilu_fctint'
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if(psb_get_errstatus().ne.0) return
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info=0
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call psb_erractionsave(err_act)
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call psb_nullify_sp(trw)
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trw%m=0
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trw%k=0
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if(debug) write(0,*)'LUINT Allocating TRW'
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call psb_sp_all(trw,1,info)
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if(info.ne.0) then
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info=4010
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ch_err='psb_sp_all'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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if(debug) write(0,*)'LUINT Done Allocating TRW'
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lia2(1) = 1
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uia2(1) = 1
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l1 = 0
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l2 = 0
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m = ma+mb
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if(debug) write(0,*)'In DCSRLU Begin cycle',m,ma,mb
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!
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! Cycle over the matrix rows
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!
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do i = 1, m
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if(debug) write(0,*)'LUINT: Loop index ',i,ma
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d(i) = dzero
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if (i <= ma) then
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!
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! Copy the i-th local row of the matrix, stored in a,
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! into laspk/d(i)/uaspk
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!
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call ilu_copyin(i,ma,a,i,1,m,l1,lia1,lia2,laspk,&
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& d(i),l2,uia1,uia2,uaspk,ktrw,trw)
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else
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!
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! Copy the i-th local row of the matrix, stored in b
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! (as (i-ma)-th row), into laspk/d(i)/uaspk
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!
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call ilu_copyin(i-ma,mb,b,i,1,m,l1,lia1,lia2,laspk,&
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& d(i),l2,uia1,uia2,uaspk,ktrw,trw)
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endif
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lia2(i+1) = l1 + 1
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uia2(i+1) = l2 + 1
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dia = d(i)
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do kk = lia2(i), lia2(i+1) - 1
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!
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! Compute entry l(i,k) (lower factor L) of the incomplete
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! factorization
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!
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temp = laspk(kk)
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k = lia1(kk)
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laspk(kk) = temp*d(k)
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!
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! Update the rest of row i (lower and upper factors L and U)
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! using l(i,k)
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!
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low1 = kk + 1
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low2 = uia2(i)
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!
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updateloop: do jj = uia2(k), uia2(k+1) - 1
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!
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j = uia1(jj)
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!
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if (j < i) then
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!
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! search l(i,*) (i-th row of L) for a matching index j
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!
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do ll = low1, lia2(i+1) - 1
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l = lia1(ll)
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if (l > j) then
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low1 = ll
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exit
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else if (l == j) then
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laspk(ll) = laspk(ll) - temp*uaspk(jj)
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low1 = ll + 1
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cycle updateloop
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end if
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enddo
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else if (j == i) then
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!
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! j=i: update the diagonal
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!
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dia = dia - temp*uaspk(jj)
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cycle updateloop
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!
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else if (j > i) then
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!
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! search u(i,*) (i-th row of U) for a matching index j
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!
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do ll = low2, uia2(i+1) - 1
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l = uia1(ll)
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if (l > j) then
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low2 = ll
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exit
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else if (l == j) then
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uaspk(ll) = uaspk(ll) - temp*uaspk(jj)
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low2 = ll + 1
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cycle updateloop
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end if
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enddo
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end if
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!
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! If we get here we missed the cycle updateloop, which means
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! that this entry does not match; thus we accumulate on the
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! diagonal for MILU.
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!
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if (ialg == mld_milu_n_) then
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dia = dia - temp*uaspk(jj)
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end if
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enddo updateloop
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enddo
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!
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! Check pivot size
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!
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if (abs(dia) < epstol) then
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!
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! Too small pivot: unstable factorization
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!
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info = 2
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int_err(1) = i
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write(ch_err,'(g20.10)') abs(dia)
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call psb_errpush(info,name,i_err=int_err,a_err=ch_err)
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goto 9999
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else
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!
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! Compute 1/pivot
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!
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dia = done/dia
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end if
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d(i) = dia
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!
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! Scale row i of upper triangle
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!
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do kk = uia2(i), uia2(i+1) - 1
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uaspk(kk) = uaspk(kk)*dia
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enddo
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enddo
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call psb_sp_free(trw,info)
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if(info.ne.0) then
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info=4010
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ch_err='psb_sp_free'
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call psb_errpush(info,name,a_err=ch_err)
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goto 9999
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end if
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if(debug) write(0,*)'Leaving ilu_fct'
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call psb_erractionrestore(err_act)
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return
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9999 continue
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call psb_erractionrestore(err_act)
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if (err_act.eq.psb_act_abort_) then
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call psb_error()
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return
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end if
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return
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end subroutine mld_dilu_fctint
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!
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! Subroutine: ilu_copyin.
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|
! Version: real.
|
|
! Note: internal subroutine of mld_dilu_fct.
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|
!
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|
! Copies a row of a sparse matrix A, stored into the psb_dspmat_type data
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|
! structure a, into the arrays laspk, dia, uaspk, corresponding to the lower
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! triangle, the diagonal and the upper triangle of A. The entries in the three
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|
! arrays are stored according to the CSR format.
|
|
!
|
|
! If the sparse matrix is in CSR format, a 'straight' copy is performed;
|
|
! otherwise psb_sp_getblk is used to extract a block of rows, which is then
|
|
! copied into laspk, dia, uaspk row by row, through successive calls to
|
|
! ilu_copyin
|
|
!
|
|
! This routine is used by mld_dilu_fctin (contained into mld_dilu_fct) in the
|
|
! computation of the ILU(0) factorization of a local sparse matrix.
|
|
!
|
|
! TODO: modify the routine to allow copying into output L and U that are already
|
|
! filled with indices; this would allow computing an ILU(K) pattern, then use
|
|
! the ILU(0) internal for subsequente calls with the same pattern.
|
|
!
|
|
! Arguments:
|
|
! i - integer, input.
|
|
! The local index of the row to be extracted from the
|
|
! sparse matrix structure a.
|
|
! m - integer, input
|
|
! The number of rows of the local matrix stored into a.
|
|
! a - type(<psb_dspmat_type>), input.
|
|
! The sparse matrix structure containing the row to be copied.
|
|
! jd - integer, input
|
|
! The column index of the diagonal entry of the row to be
|
|
! copied.
|
|
! jmin - integer, input
|
|
! Minimum valid column index.
|
|
! jmax - integer, input
|
|
! Maximum valid column index.
|
|
! The output matrix will contain a clipped copy
|
|
! taken from A(1:M,JMIN:JMAX)
|
|
! l1 - integer, inout
|
|
! Pointer to the last occupied entry of the row copied in laspk.
|
|
! lia1 - integer, dimension(:), inout
|
|
! The column indices of the nonzero entries of the lower triangle
|
|
! copied in laspk row by row (see mld_dilu_fctint), according
|
|
! to the CSR storage format.
|
|
! lia2 - integer, dimension(:), inout
|
|
! The indices identifying the first nonzero entry of each row
|
|
! of the lower triangle copied in laspk row by row (see
|
|
! mld_dilu_fctint), according to the CSR storage format.
|
|
! laspk - real(kind(1.d0)), dimension(:), inout
|
|
! The array where the entries of the row corresponding to the
|
|
! lower triangle are copied.
|
|
! dia - real(kind(1.d0)), output
|
|
! The diagonal element of the copied row.
|
|
! l2 - integer, inout
|
|
! Pointer to the last occupied entry of the row copied in uaspk.
|
|
! uia1 - integer, dimension(:), inout
|
|
! The column indices of the nonzero entries of the upper triangle
|
|
! copied in uaspk row by row (see mld_dilu_fctint), according
|
|
! to the CSR storage format.
|
|
! uia2 - integer, dimension(:), inout
|
|
! The indices identifying the first nonzero entry of each row
|
|
! of the upper triangle copied in uaspk row by row (see
|
|
! mld_dilu_fctint), according to the CSR storage format.
|
|
! uaspk - real(kind(1.d0)), dimension(:), inout
|
|
! The array where the entries of the row corresponding to the
|
|
! upper triangle are copied.
|
|
! ktrw - integer, inout
|
|
! The index identifying the last entry taken from the
|
|
! staging buffer trw. See below.
|
|
! trw - type(psb_dspmat_type), inout
|
|
! A staging buffer. If the matrix A is not in CSR format, we use
|
|
! the psb_sp_getblk routine and store its output in trw; when we
|
|
! need to call getblk we do it for a block of rows, and then we consume
|
|
! them from trw in successive calls to this routine, until we empty the
|
|
! buffer. Thus we will make a call to geblk every NB calls to copyin.
|
|
! If A is in CSR format it is unused.
|
|
!
|
|
subroutine ilu_copyin(i,m,a,jd,jmin,jmax,l1,lia1,lia2,laspk,&
|
|
& dia,l2,uia1,uia2,uaspk,ktrw,trw)
|
|
|
|
use psb_base_mod
|
|
|
|
implicit none
|
|
|
|
! Arguments
|
|
type(psb_dspmat_type) :: a,trw
|
|
integer :: i,m,ktrw,jd,jmin,jmax,l1,l2
|
|
integer :: lia1(:),lia2(:),uia1(:),uia2(:)
|
|
real(kind(1.d0)) :: laspk(:), uaspk(:), dia
|
|
|
|
! Local variables
|
|
type(psb_int_heap) :: heap
|
|
integer :: k,j,info,irb
|
|
integer, parameter :: nrb=16
|
|
character(len=20), parameter :: name='mld_dilu_fctint'
|
|
character(len=20) :: ch_err
|
|
|
|
if (psb_get_errstatus() /= 0) return
|
|
info=0
|
|
call psb_erractionsave(err_act)
|
|
|
|
if (toupper(a%fida)=='CSR') then
|
|
|
|
!
|
|
! Take a fast shortcut if the matrix is stored in CSR format
|
|
!
|
|
|
|
do j = a%ia2(i), a%ia2(i+1) - 1
|
|
k = a%ia1(j)
|
|
! write(0,*)'KKKKK',k
|
|
if ((k < jd).and.(k >= jmin)) then
|
|
l1 = l1 + 1
|
|
laspk(l1) = a%aspk(j)
|
|
lia1(l1) = k
|
|
else if (k == jd) then
|
|
dia = a%aspk(j)
|
|
else if ((k > jd).and.(k <= jmax)) then
|
|
l2 = l2 + 1
|
|
uaspk(l2) = a%aspk(j)
|
|
uia1(l2) = k
|
|
end if
|
|
enddo
|
|
|
|
else
|
|
|
|
!
|
|
! Otherwise use psb_sp_getblk, slower but able (in principle) of
|
|
! handling any format. In this case, a block of rows is extracted
|
|
! instead of a single row, for performance reasons, and these
|
|
! rows are copied one by one into laspk, dia, uaspk, through
|
|
! successive calls to ilu_copyin
|
|
!
|
|
|
|
if ((mod(i,nrb) == 1).or.(nrb==1)) then
|
|
irb = min(m-i+1,nrb)
|
|
call psb_sp_getblk(i,a,trw,info,lrw=i+irb-1)
|
|
if(info.ne.0) then
|
|
info=4010
|
|
ch_err='psb_sp_getblk'
|
|
call psb_errpush(info,name,a_err=ch_err)
|
|
goto 9999
|
|
end if
|
|
ktrw=1
|
|
end if
|
|
|
|
do
|
|
if (ktrw > trw%infoa(psb_nnz_)) exit
|
|
if (trw%ia1(ktrw) > i) exit
|
|
k = trw%ia2(ktrw)
|
|
if ((k < jd).and.(k >= jmin)) then
|
|
l1 = l1 + 1
|
|
laspk(l1) = trw%aspk(ktrw)
|
|
lia1(l1) = k
|
|
else if (k == jd) then
|
|
dia = trw%aspk(ktrw)
|
|
else if ((k > jd).and.(k <= jmax)) then
|
|
l2 = l2 + 1
|
|
uaspk(l2) = trw%aspk(ktrw)
|
|
uia1(l2) = k
|
|
end if
|
|
ktrw = ktrw + 1
|
|
enddo
|
|
|
|
end if
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act.eq.psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
end subroutine ilu_copyin
|
|
|
|
end subroutine mld_dilu_fct
|